Brownian motion electric field

Ions of an electrolyte are free to move about in solution by Brownian motion and, depending on the charge, have specific direction of motion under the influence of an external electric field. The movement of the ions under the influence of an electric field is responsible for the current flow through the electrolyte. The velocity of migration of an ion is given by ... 

Consider now the observed values of the equivalent conductivity for the various species of ions given in Table 2 [disregarding the ions (OH)-and H+, which need special consideration]. If we ask, from this point of view, why such a wide variety of values is found, this must be ascribed to the wide variety in the character of the random motion executed by different species of ions in the absence of an electric field. We shall not go into the details of Einstein s theory of the Brownian motion but the liveliness of the motion for any species of particle may be expressed by assigning a value to a certain parameter for a charged particle in an... 

Hydrophobic colloidal particles move readily in the liqnid phase under the effect of thermal motion of the solvent molelcnles (in this case the motion is called Brownian) or under the effect of an external electric field. The surfaces of such particles as a rule are charged (for the same reasons for which the snrfaces of larger metal and insnlator particles in contact with a solution are charged). As a result, an EDL is formed and a certain valne of the zeta potential developed. 

The principal axis of the cone represents the component of the dipole under the influence of the thermal agitation. The component of the dipole in the cone results from the field that oscillates in its polarization plane. In this way, in the absence of Brownian motion the dipole follows a conical orbit. In fact the direction of the cone changes continuously (because of the Brownian movement) faster than the oscillation of the electric field this leads to chaotic motion. Hence the structuring effect of electric field is always negligible, because of the value of the electric field strength, and even more so for lossy media. 

Brownian motion, other mechanisms, as for instance, a decay of a local vibration into substrate phonons (see Chapter 4) or inhomogeneous broadening caused by static shifts of oscillator frequencies in random electric fields of a disordered dipole environment. A temperature dependence of a broadening arising from these additional effects should be considerably weaker than the exponential dependence in Eq. (A2.26) or (A2.4). The total broadening is therefore expressible as... 

Let us apply the interpolation procedure to a case involving an electric field. It is well known that the efficiency of the granular bed filters can be significantly increased by applying an external electrostatic field across the filter. In this case, fine (<0.5-/rm) particles deposit on the surface of the bed because of Brownian motion as well as because of the electrostatically generated dust particle drift [51], The rate of deposition can be calculated easily for a laminar flow over a sphere in the absence of the electrostatic field [5]. The other limiting case, in which the motion of the particles is exclusively due to the electric field, could also be treated [52], When, however, the two effects act simultaneously, only numerical solutions to the problem could be obtained [51],... 

Applying the laws of Brownian motion to the distribution of free ions and ion-pairs in the presence of a external electric field Onsager calculated the rate constants of recombination and dissociation for equilibrium [1] as ... 

Electrophoretic migrations are always superimposed on other displacements, which must either be eliminated or corrected to give accurate values for mobility. Examples of these other kinds of movement are Brownian motion, sedimentation, convection, and electroosmotic flow. Brownian motion, being random, is eliminated by averaging a series of individual observations. Sedimentation and convection, on the other hand, are systematic effects. Corrections for the former may be made by observing a particle with and without the electric field, and the latter may be minimized by effective thermostating and working at low current densities. 

Applications of optical methods to study dilute colloidal dispersions subject to flow were pioneered by Mason and coworkers. These authors used simple turbidity measurements to follow the orientation dynamics of ellipsoidal particles during transient shear flow experiments [175,176], In addition, the superposition of shear and electric fields were studied. The goal of this work was to verify the predictions of theories predicting the orientation distributions of prolate and oblate particles, such as that discussed in section 7.2.I.2. This simple technique clearly demonstrated the phenomena of particle rotations within Jeffery orbits, as well as the effects of Brownian motion and particle size distributions. The method employed a parallel plate flow cell with the light sent down the velocity gradient axis. 

Photon Correlation. Particles suspended in a fluid undergo Brownian motion due to collisions with the liquid molecules. This random motion results in scattering and Doppler broadening of the frequency of the scattered light. Experimentally, it is more accurate to measure the autocorrelation function in the time domain than measuring the power spectrum in the frequency domain. The normalized electric field autocorrelation function g(t) for a suspension of monodisperse particles or droplets is given by ... 

In addition to these more practical problems of catalyst preparation, there are also severe theoretical problems associated with the prediction of the chemistry in the fluid state of a compound. The motion of all structural elements (atoms, ions, molecules) is controlled by a statistical contribution from Brownian motion, by gradients of the respective chemical potentials (those of the structural elements and those of all species such as oxygen or water in the gas phase which can react with the structural elements and thus modify the local concentration), and by external mechanical forces such as stirring and gas evolution. In electric fields (as in an arc melting furnace), field effects will further contribute to nonisotropic motion and thus to the creation of concentration gradients. An exhaustive treatment of these problems can be found in a textbook [6] and in the references therein. 

In diffusion charging, particles are charged by unipolar ions (ions having the same sign) in the absence of an applied electric field. Collisions of ions and particles occur as a result of random thermal motion of the ions, the brownian motion of the particles being generally neglected. 

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